×

zbMATH — the first resource for mathematics

On pexiderized Jensen-Hosszú functional equation on the unit interval. (English) Zbl 1306.39020
Summary: We solve the functional equation of the form \[ 2f\biggl(\frac{x+y}{2}\biggl)=g(x+y-xy)+h(xy) \] in the class of real functions defined on the unit interval \([0,1]\). We prove that it is not stable, but if two functions from the triple \(\{f,g,h\}\) coincides the analogue equation is stable in the Hyers-Ulam sense.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Kominek, Z., On a Jensen-hosszú equation I, Ann. Math. Sil., 23, 57-60, (2009) · Zbl 1229.39032
[2] Kominek, Z., On the Hyers-Ulam stability of Pexider-type extension of the Jensen-hosszú equation, Bull. Int. Virtual Inst., 1, 53-57, (2011), (Former: Bull. Soc. Math. Banja Luka) · Zbl 1441.39030
[3] Kominek, Z.; Sikorska, J., On Jensen-Hosszú Equation II, Vol. 15(1), 61-67, (2012), MIA · Zbl 1382.39030
[4] Kuczma, M., An introduction to the theory of functional equations and inequalities. cauchy’s equation and jensen’s inequality, (1985), PWN Uniwersytet Śląski Warszawa-Kraków-Katowice · Zbl 0555.39004
[5] Laczkovich, M., The local stability of convexity, affinity and of the Jensen equation, Aequationes Math., 58, 1-2, 135-142, (1999) · Zbl 0934.39013
[6] Losonczi, L., On the stability of hosszú functional equation, Results Math., 29, 305-310, (1996) · Zbl 0872.39017
[7] Tabor, J., Hosszú functional equation on the unit interval is not stable, Publ. Math. Debrecen, 49, 3-4, 335-340, (1996) · Zbl 0870.39012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.